CN104063838B - Asymmetric Watermarking Schemes method based on Logistic chaotic maps and Walsh sequences - Google Patents
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Abstract
The invention provides a kind of Asymmetric Watermarking Schemes algorithm based on Logistic chaotic maps and Walsh sequences, comprise the following steps：Eigenmatrix is obtained according to the maximum singular value of every piece of carrier image coefficient block；It is public key watermark to choose with the incoherent Walsh sequences of eigenmatrix, kinetics equation is mapped according to Logistic and obtains chaos sequence, the chaos sequence is converted to sequence that value is ± 1 and one and the incoherent sequence of eigenmatrix is therefrom intercepted is used as private key watermark；Obtain being embedded in watermark according to the weighted sum of public key watermark and private key watermark, watermarking images are generated according to the information of embedded watermark；Watermarking images are detected.Technical scheme is safe, can preferably protect copyright, and detection performance is good, strong robustness.
Description
Technical Field
The invention belongs to the technical field of digital watermarking, and particularly relates to an asymmetric watermarking method based on Logistic chaotic mapping and a Walsh sequence.
Background
With the wide popularization of digital products and the rapid development of network technologies, the security problem of digital products is more and more emphasized by people. How to effectively protect the copyright of a product becomes a great concern.
The digital watermarking technology can well protect the copyright of digital products. However, the digital watermarking technology generally adopts symmetric watermarking, for the traditional symmetric digital watermarking technology, the same secret key is adopted for watermark embedding and watermark detection, watermark detection can only be completed by a copyright owner and an authorized institution, and when copyright disputes occur, the copyright owner needs to show a private secret key to prove that the copyright owner has the legal copyright. Once the key is exposed, an attacker can remove or forge the watermark, which does not protect the copyright well.
Disclosure of Invention
The invention aims to provide an asymmetric watermarking method based on Logistic chaotic mapping and a Walsh sequence, so as to solve the problems.
In order to achieve the purpose, the invention adopts the technical scheme that:
an asymmetric watermarking method based on Logistic chaotic mapping and a Walsh sequence is characterized by comprising the following steps:
the method comprises the following steps: construction of the feature matrix S
Take image A of m × mm×mAs a carrier image, the carrier image is subjected to DCT conversion, 4k × 4k intermediate frequency coefficients are selected from DCT coefficients to form a matrix B4k×4k，
Will matrix B4k×4kDividing the image into N blocks of 4 × 4 coefficients which are not overlapped with each other, wherein N is k × k,
denote the i-th block coefficient block as Bi，i∈[1,N]According to [ u ]i,si,vi]＝svd(Bi) Performing singular value decomposition on each coefficient block, extracting the maximum singular value of each coefficient block to obtain N maximum singular values in total, and forming a characteristic matrix S by the N maximum singular values;
step two: public key watermark WpAnd private key watermark WsConstruction of
Selecting Walsh sequences of length N not related to the feature matrix S as public key watermarks WpI.e. by
Mapping kinetic equation x according to Logisticn+1＝μ0xn(1-xn) Obtaining a chaos sequence X ═ X1,x2,Λ,xnIn the formula, mu0Is a branch parameter, mu0∈ (0,4), initial value x of x0∈(0,1)，
According to xi＝mod(round(xi×108),2)，The chaotic sequence X is converted into a sequence with the value of +/-1, mod represents modular operation, round represents nearest rounding,
intercepting a sequence Y with the length of N irrelevant to the feature matrix S from sequences with the value of +/-1 ═ Y1,y2,Λ,yNAs private key watermark WsI.e. by
The public key watermark WpAnd private key watermark WsThe construction of the method is not in sequence;
step three: generating watermark image A'm×m
Computing public key watermark WpAnd private key watermark WsIs constructed from a weighted sum to obtain an embedded watermark Ww，
According to S' ═ S + lambda WwTo embed watermark WwThe information is embedded into the feature matrix S by adopting addition to obtain a feature matrix S ', and the feature matrix S' is matched with the feature matrixPerforming singular value inverse transformation on a singular value corresponding to each coefficient block in the matrix S ' to obtain a modified DCT coefficient, and performing DCT inverse transformation on the carrier image by using the modified DCT coefficient to obtain a watermark image A ' of m × m 'm×m；
Step four: watermark detection
To watermark image A'm×mObtaining a characteristic matrix S 'by adopting the operation of the step one, wherein the characteristic matrix S' is S + lambda Ww+n0＝S+λ(αWs+βWp)+n0，n0Representing the interference signals caused by various attacks,
by the use of Wp_threshold、WsThreshold represents a public key detection threshold and a private key detection threshold respectively,
public key detection threshold WpThe setting method of the threshold comprises the following steps:wherein,is the mean value of the feature matrix S,watermarking W for public keyspThe average value of (a) of (b),watermarking W for public keyspThe energy of (a) is,
detecting the threshold value W according to the public keypMethod for setting a threshold value W for detecting a private keys_threshold，
By the use of Wp_test、WsTest represents the detection value of the public key detection and the detection value of the private key detection respectively, and according to the formula:
calculating to obtain WpW is calculated by referring to the same calculation methods_test，
W is to bepTest and WpA threshold is compared when Wp_test≥WpThreshold, then determine the public key watermark WpIf the watermark exists, otherwise, the public key watermark W is judgedpIn the absence of the presence of the agent,
w is to besTest and WsA threshold is compared when Ws_test≥WsA threshold, then the private key watermark W is determinedsIf the watermark exists, otherwise, the private key watermark W is judgedsIs absent.
The technical scheme of the invention is further characterized in that: in step one, the DCT coefficients are scanned in a zigzag manner, and the DCT coefficients are sorted from low to high according to frequency.
The technical scheme of the invention is further characterized in that: image Am×mIs a gray scale image.
The technical scheme of the invention is further characterized in that: step two branch parameter mu0The value range of (d) is 3.5699456 ≤ μ0≤4。
The technical scheme of the invention is further characterized in that: embedding watermark W in step threewThe construction method comprises the following steps: ww＝αWs+βWpWherein α (0, 1).
Compared with the background art, the technical scheme of the invention has the following advantages and positive effects:
1. high safety and better copyright protection
According to the technical scheme provided by the invention, public key watermark W is adoptedpAnd private key watermark WsCompared with the background technology, the embedded watermark is constructed by the weighted sum, and the copyright owner does not need to expose the private key watermark when copyright dispute occurs, and can directly benefitThe public key watermark is used for detection, and even if a watermark attacker masters the private key watermark, the embedded key cannot be deduced.
2. Good detection performance and strong robustness
The technical scheme of the invention adopts an asymmetric watermarking method based on Logistic chaotic mapping and Walsh sequence to embed the watermark into the carrier image, has good detection performance and has good robustness to attacks such as additive noise, lossy compression, cutting and the like.
Drawings
FIG. 1 is a carrier image in an embodiment of the present invention;
fig. 2 is a flowchart of watermark embedding in an embodiment of the present invention;
fig. 3 is a watermark detection flow chart in an embodiment of the technical solution of the present invention;
fig. 4 is a watermark image in an embodiment of the present invention;
FIG. 5 shows a watermark detection result under JPEG compression in an embodiment of the present invention; and
fig. 6 is an explanatory diagram of detection results of different detection sequences when gaussian noise is added in the embodiment of the present invention.
Detailed Description
The asymmetric watermarking method based on Logistic chaotic mapping and Walsh sequences according to the present invention is further described with reference to the accompanying drawings.
< example >
Fig. 1 is a carrier image in an embodiment of the present invention.
This embodiment is as followsIn matlab 2013a environment, a gray image 512 × 512 shown in fig. 1 is used as a carrier image (i.e., m is 512), and a branch parameter μ of a one-dimensional Logistic chaotic sequence is taken03.711 initial value x00.773. Public key WpThe Walsh sequence formed by line 112 of the Hadamard matrix of 4096 × 4096 is selected for embedding the watermark WwWhen the parameter α is 0.73, β is 0.64, and λ is 17.
Fig. 2 is a flowchart of watermark embedding in an embodiment of the present invention.
Fig. 3 is a watermark detection flowchart in an embodiment of the technical solution of the present invention.
In the asymmetric watermarking method based on Logistic chaotic mapping and Walsh sequence provided in this embodiment, firstly, a watermark is embedded by using the Logistic chaotic mapping and Walsh sequence, and then the watermark is embedded into a feature matrix formed by the maximum singular value of a carrier image, and a correlation value calculation method is used to detect the watermark. The method specifically comprises the following steps as shown in fig. 2 and 3:
the method comprises the following steps: construction of the feature matrix S
Take image A of m × m as shown in FIG. 1m×mAs a carrier image, m is 512, the carrier image is DCT-converted, DCT coefficients are' zigzag-scanned, and 4k × 4k intermediate frequency coefficients are selected from the DCT coefficients to form a matrix B4k×4k，
Will matrix B4k×4kDividing the block into N non-overlapping 4 × 4 coefficient blocks, wherein N is k × k, and the i-th coefficient block is marked as Bi，i∈[1,N]According to [ u ]i,si,vi]＝svd(Bi) Performing singular value decomposition on each coefficient block and extracting the maximum singular value, i.e. s, of each blockiAnd (1,1) obtaining N maximum singular values in total, and forming the N maximum singular values into a feature matrix S.
Step two: public key watermark WpAnd private key watermark WsConstruction of
Selection and characterizationThe uncorrelated Walsh sequences of the matrix S of length N are public key watermarks WpI.e. by
Taking the branch parameter mu03.711 initial value x0Substituting Logistic mapping kinetic equation x into 0.773n+1＝μ0xn(1-xn) In (2), obtain chaos sequence X ═ { X ═ X1,x2,Λ,xn}。
According to xi＝mod(round(xi×108),2)，And converting the chaotic sequence X into a sequence with the value of +/-1, wherein mod represents modulo operation, and round represents nearest rounding.
Intercepting a sequence Y with the length of N irrelevant to the feature matrix S from sequences with the value of +/-1 ═ Y1,y2,Λ,yNAs private key watermark WsI.e. by
Fig. 4 shows a watermark image according to an embodiment of the present invention.
Step three: generating watermark image A'm×m
The parameters α, β, and λ are set to 0.73, 0.64, and 17, respectively.
Watermarking W with public keypAnd private key watermark WsTo construct an embedded watermark Ww，Ww＝αWs+βWp。
According to S' ═ S + lambda WwTo embed watermark WwThe information is embedded into the characteristic matrix S by adopting addition to obtain a characteristic matrix S ', and singular value inverse transformation is carried out on the singular value corresponding to each coefficient block in the characteristic matrix S' to obtain a modified valuePerforming DCT inverse transformation on the carrier image by using the modified DCT coefficient to obtain a watermark image A 'of m × m shown in FIG. 4'm×m。
Step four: watermark detection
To watermark image A'm×mObtaining a characteristic matrix S 'by adopting the operation of the step one, wherein the characteristic matrix S' is S + lambda Ww+n0＝S+λ(αWs+βWp)+n0，n0Representing the interference signals caused by various attacks,
by the use of Wp_threshold、WsThreshold represents a public key detection threshold and a private key detection threshold respectively,
public key detection threshold WpThe setting method of the threshold comprises the following steps:wherein,is the mean value of the feature matrix S,watermarking W for public keyspThe average value of (a) of (b),watermarking W for public keyspThe energy of (a) is,
detecting the threshold value W according to the public keypMethod for setting a threshold value W for detecting a private keys_threshold，
By the use of Wp_test、WsTest represents the detection value of the public key detection and the detection value of the private key detection respectively, and according to the formula:
due to the structure of Wp、WsSatisfies the following relationship with the feature matrix S:
then:public key detection threshold WpA threshold is set as:whereinIs the average of all the elements in the feature matrix S,is the average of the public keys and,is the energy of the public key. Similarly, the detection threshold value W of the private key can be obtaineds_threshold。
W is to bepTest and WpA threshold is compared when Wp_test≥WpThreshold, then determine the public key watermark WpIf the watermark exists, otherwise, the public key watermark W is judgedpIs absent; w is to besTest and WsA threshold is compared when Ws_test≥WsA threshold, then the private key watermark W is determinedsIf the watermark exists, otherwise, the private key watermark W is judgedsIs absent.
For watermark image A 'shown in FIG. 4'm×mAnd carrying out attacks such as JPEG compression, Gaussian noise addition, salt and pepper noise addition, shearing and the like.
Fig. 5 shows watermark detection results under JPEG compression in an embodiment of the present invention.
JPEG compression: to pairWatermark image A 'shown in FIG. 4'm×mJPEG compression processing is performed to different degrees, and then watermark detection is performed, and the detection effect is shown in fig. 5. As can be seen from fig. 5, JPEG compression with a quality factor of 20% is performed on the watermark image, so that the public key detection and the private key detection are still effective, and the detection performance is good.
Gaussian noise:
(1) for watermark image A 'shown in FIG. 4'm×mGaussian noise was added, the variance of the noise was 0.006, 0.009, 0.012, respectively, and the watermark detection results are shown in table 1. As can be seen from table 1, the method provided by this embodiment has better capability of resisting gaussian noise interference.
TABLE 1 detection of watermarks after Gaussian noise addition
Fig. 6 is an explanatory diagram of detection results of different detection sequences when gaussian noise is added in the embodiment of the present invention.
(2) For watermark image A 'shown in FIG. 4'm×mGaussian noise is added, the noise variance is 0.009, 1000 sequences are used for detection, wherein the 200 th detection sequence is private key watermark, the 400 th detection sequence is public key watermark, and the other detection sequences are 998 Walsh sequences formed by the 200 th row to the 1197 th row of a Hadamard matrix of 4096 × 4096, and the watermark detection result is shown in FIG. 6.
Salt and pepper noise: for watermark image A 'shown in FIG. 4'm×mThe noise intensities of salt and pepper noise were 0.01, 0.03, and 0.04, respectively, and the watermark detection results are shown in table 2. As can be seen from Table 2, the method of the present invention has a better resistance to salt and pepper noise interference.
Table 2 detection results of watermarks after adding salt and pepper noises of different strengths
Shearing: for watermark image A 'shown in FIG. 4'm×mThe cropping is performed to different degrees and the watermark detection results are shown in table 3. As can be seen from Table 3, the process of the present invention has a better shear resistance.
Table 3 detection results of clipped watermarks of different degrees
Compared with the background art, the technical scheme provided by the embodiment has the following advantages and positive effects:
1. high safety and better copyright protection
According to the technical scheme provided by the embodiment, public key watermark W is adoptedpAnd private key watermark WsCompared with the background technology, when copyright disputes occur, a copyright owner does not need to expose the private key watermark and can directly detect the private key watermark by using the public key watermark, and even if a watermark attacker masters the private key watermark, the embedded key cannot be deduced.
2. Good detection performance and strong robustness
The technical scheme provided by the embodiment adopts an asymmetric watermarking method based on Logistic chaotic mapping and Walsh sequences to embed watermarks into a carrier image, and JPEG compression, Gaussian noise adding, salt and pepper noise adding, shearing and other attack tests show that the technical scheme provided by the embodiment has good detection performance and has good robustness to attacks such as additive noise, lossy compression, shearing and the like.
Of course, the asymmetric watermarking method based on Logistic chaotic mapping and Walsh sequence according to the present invention is not limited to the above embodiments. The above description is only a basic description of the present invention, and any equivalent changes made according to the technical solution of the present invention belong to the protection scope of the present invention.
In addition, in the above embodiment, a gray scale image of 512 × 512 is selected as the carrier image, and according to the technical scheme of the present invention, a square image of any length can be selected as the carrier image, and the square image can be a gray scale image or a color image, which can achieve the same effect.
In addition, in the above-described embodiment, the branch parameter μ03.711 initial value x00.773, the technical scheme of the invention branches from the parameter mu0May be selected from any number between 0 and 4, x0Can be selected from any value between 0 and 1, and can achieve the same action and effect.
In the above embodiment, the parameter α is 0.73 and the parameter β is 0.64, and the parameters α and β in the present invention may be selected from any values between 0 and 1, and the same effects can be achieved.
Claims (4)
1. An asymmetric watermarking method based on Logistic chaotic mapping and a Walsh sequence is characterized by comprising the following steps:
the method comprises the following steps: construction of the feature matrix S
Take image A of m × mm×mAs a carrier image, performing DCT conversion on the carrier image, selecting 4k × 4k intermediate frequency coefficients from DCT coefficients to form a matrix B4k×4k，
The matrix B4k×4kDividing the image into N blocks of 4 × 4 coefficients which are not overlapped with each other, wherein N is k × k,
will be firsti blocks the coefficient block is marked as Bi，i∈[1,N]According to [ u ]i,si,vi]＝svd(Bi) Performing singular value decomposition on each coefficient block, extracting the maximum singular value of each coefficient block to obtain N maximum singular values in total, and forming a feature matrix S by the N maximum singular values;
step two: public key watermark WpAnd private key watermark WsConstruction of
Selecting a Walsh sequence with the length of N irrelevant to the characteristic matrix S as a public key watermark WpI.e. by
Mapping kinetic equation x according to Logisticn+1＝μ0xn(1-xn) Obtaining a chaos sequence X ═ X1,x2,Λ,xnIn the formula, mu0Is a branch parameter, mu0∈ (0,4), initial value x of x0∈(0,1)，
According to xi＝mod(round(xi×108),2)，Converting the chaotic sequence X into a sequence with the value of +/-1, wherein mod represents modular operation, round represents nearest rounding,
intercepting a sequence Y with the length of N irrelevant to the feature matrix S from sequences with the value of +/-1 ═ Y1,y2,Λ,yNAs private key watermark WsI.e. by
The public key watermark WpAnd private key watermark WsThe construction of the method is not in sequence;
step three: generating watermark image A'm×m
Computing the public key watermark WpAnd said private key watermark WsIs constructed to obtain an embedded watermark W based on the weighted sumwThe embedded watermark WwThe construction method comprises the following steps: ww＝αWs+βWpα, β are both preset parameters, α (0, 1),
according to S' ═ S + lambda Wwλ is a preset parameter, and embedding the watermark WwThe information of (2) is embedded into the feature matrix S by adopting addition to obtain a feature matrix S ', singular value inverse transformation is carried out on a singular value corresponding to each coefficient block in the feature matrix S' to obtain a modified DCT coefficient, and the DCT inverse transformation is carried out on the carrier image by adopting the modified DCT coefficient to obtain a watermark image A 'of m × m'm×m；
Step four: watermark detection
To the watermark image A'm×mObtaining a characteristic matrix S 'by adopting the operation of the step one, wherein the characteristic matrix S' -S + lambda WW+n0＝S+λ(αWs+βWp)+n0，n0Representing the interference signals caused by various attacks,
by the use of Wp_threshold、WsThreshold represents a public key detection threshold and a private key detection threshold respectively,
the public key detection threshold WpThe setting method of the threshold comprises the following steps:wherein,is the mean value of the feature matrix S,watermarking W for the public keypThe average value of (a) of (b),watermarking W for the public keypThe energy of (a) is,
detecting the threshold value W according to the public keypA method for setting a threshold value W for detecting the private keys_threshold，
By the use of Wp_test、WsTest represents the detection value of the public key detection and the detection value of the private key detection respectively, and according to the formula:
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>W</mi> <mi>p</mi> </msub> <mo>_</mo> <mi>t</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <msup> <msub> <mi>W</mi> <mi>p</mi> </msub> <mi>T</mi> </msup> <mo>*</mo> <msup> <mi>S</mi> <mrow> <mo>&prime;</mo> <mo>&prime;</mo> </mrow> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <msup> <msub> <mi>W</mi> <mi>p</mi> </msub> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>S</mi> <mo>+</mo> <mi>&lambda;</mi> <mo>(</mo> <msub> <mi>&alpha;W</mi> <mi>s</mi> </msub> <mo>+</mo> <msub> <mi>&beta;W</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>n</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <msup> <msub> <mi>W</mi> <mi>p</mi> </msub> <mi>T</mi> </msup> <mo>*</mo> <mi>S</mi> <mo>+</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <msup> <msub> <mi>W</mi> <mi>p</mi> </msub> <mi>T</mi> </msup> <mo>*</mo> <msub> <mi>n</mi> <mn>0</mn> </msub> <mo>+</mo> <mfrac> <mrow> <mi>&lambda;</mi> <mi>&alpha;</mi> </mrow> <mi>N</mi> </mfrac> <msup> <msub> <mi>W</mi> <mi>p</mi> </msub> <mi>T</mi> </msup> <mo>*</mo> <msub> <mi>W</mi> <mi>s</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mfrac> <mrow> <mi>&lambda;</mi> <mi>&beta;</mi> </mrow> <mi>N</mi> </mfrac> <msup> <msub> <mi>W</mi> <mi>p</mi> </msub> <mi>T</mi> </msup> <mo>*</mo> <msub> <mi>W</mi> <mi>p</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>
the W is obtained by calculationpA _ test, said W being calculated by reference to the same calculation methods_test，
The W ispTest and said WpA threshold is compared when Wp_test≥WpA threshold, then the public key watermark W is judgedpIf the public key watermark W exists, otherwise, the public key watermark W is judgedpIn the absence of the presence of the agent,
the W issTest and said WsA threshold is compared when Ws_test≥WsA threshold, then the private key watermark W is judgedsIf the private key watermark W exists, otherwise, the private key watermark W is judgedsIs absent.
2. The asymmetric watermarking method based on Logistic chaotic mapping and Walsh sequences according to claim 1, wherein:
in the first step, the DCT coefficients are scanned in a zigzag manner, and the DCT coefficients are sorted from low to high according to frequency.
3. The asymmetric watermarking method based on Logistic chaotic mapping and Walsh sequences according to claim 1, wherein:
the image Am×mIs a gray scale image.
4. The asymmetric watermarking method based on Logistic chaotic mapping and Walsh sequences according to claim 1, wherein:
the branch parameter μ in the second step0The value range of (d) is 3.5699456 ≤ μ0＜4。
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| CN104063838A (en) | 2014-09-24 |
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